Remek was selected for the first Intercosmos mission and as such is the first person not from the USA or USSR to be launched into space. Soyuz 28 launched March 2, 1978 and docked with Salyut 6 for a week long stay. During the stay he performed a variety of experiments with the other crew members.

Remek had begun to be disliked by the Communist leadership as divorced his first wife, a daughter of a top communist
functionary. He fell from favour after the fall of the Iron Curtain due to his affliation with the old regime. Some tried to slander his character by printing pictures of him next to the former Communist leader Gustav Husak. However he said in an interview in 2001 that after 1989 the general populance did not instantly start hating him. Many recognised that Soyuz 28 was still historic and that he was treated badly by some just looking to score some political points.

Some still don't like in the Czech Republic today as he has not denounced the former regime or returned the medals awarded to him. And even though he name was mentioned when the first elections as a possible candidate for President, he is not involved in politics.

In 2001, Remek and two American astronauts, Gene Cernan and John Blaha, were involved in a helicoptor crash in the Czech Republic. Cernan and Blaha both have ancestory in the area. The Mi-8 helicoptor was forced to make an emergency landing Milevsko, 50 miles
south of Prague, after "a decline in both of the helicopter's engines' performance". They had been heading to Bernatice, 60 miles south of Prague, the hometown of Cernan's grandfather.